Asymmetric measures of association, closed data, and multivariate analysis |
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| Authors: | Michael Ed Hohn and Edward B Nuhfer |
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| Institution: | (1) West Virginia Geological and Economic Survey, P.O. Box 879, 26505 Morgantown, West Virginia, USA;(2) Present address: Geosciences Department, University of Wisconsin, 53818 Plattsville, Wisconsin, USA |
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| Abstract: | The association between constant-sum variables Xi
and Xj
expressed as percentages can be calculated as a product-moment correlation between Xi
and Xj/(100 – Xi
) and a correlation between Xj
and Xi/(100 – Xj
). An asymmetric, square matrix may be formed from these coefficients, and multivariate analysis performed by two methods: singular value decomposition and canonical decomposition. Either analysis avoids problems in the interpretation of correlation coefficients determined from closed arrays, and provides information about dependencies among the variables beyond that obtained from the usual correlation coefficient between Xi
and Xj.Two examples show the canonical decomposition to have the greater usefulness. |
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| Keywords: | constant sum variables canonical decomposition geochemical data |
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